LEADER 02621nam 2200349 450 001 9910680698603321 005 20230527213928.0 010 $a9789493296039 035 $a(CKB)26359806100041 035 $a(NjHacI)9926359806100041 035 $a(EXLCZ)9926359806100041 100 $a20230527h20222023 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNumber Fields /$fFrans Keune 210 1$aNijmegen :$cRadboud University Press,$d2022. 210 4$dİ2023 215 $a1 online resource (xv, 569 pages) $cillustrations 320 $aIncludes bibliographical references and index. 330 $aNumber Fields is a textbook for algebraic number theory. It grew out of lecture notes of master courses taught by the author at Radboud University, the Netherlands, over a period of more than four decades. It is self-contained in the sense that it uses only mathematics of a bachelor level, including some Galois theory.Part I of the book contains topics in basic algebraic number theory as they may be presented in a beginning master course on algebraic number theory. It includes the classification of abelian number fields by groups of Dirichlet characters. Class field theory is treated in Part II: the more advanced theory of abelian extensions of number fields in general. Full proofs of its main theorems are given using a 'classical' approach to class field theory, which is in a sense a natural continuation of the basic theory as presented in Part I. The classification is formulated in terms of generalized Dirichlet characters. This 'ideal-theoretic' version of class field theory dates from the first half of the twentieth century. In this book, it is described in modern mathematical language. Another approach, the 'ide?lic version', uses topological algebra and group cohomology and originated halfway the last century. The last two chapters provide the connection to this more advanced ide?lic version of class field theory. The book focuses on the abstract theory and contains many examples and exercises. For quadratic number fields algorithms are given for their class groups and, in the real case, for the fundamental unit. New concepts are introduced at the moment it makes a real difference to have them available. 606 $aAlgebraic number theory 615 0$aAlgebraic number theory. 676 $a512.74 700 $aKeune$b Frans$01359818 801 0$bNjHacI 801 1$bNjHacl 912 $a9910680698603321 996 $aNumber Fields$93374829 997 $aUNINA